Extended Multiresolution Analysis for Filtering Incomplete Heterogeneous Geophysical Time Series

Wavelet multiresolution analysis (MRA) is a widely used and effective method for filtering noisy time series and investigating the detailed characteristics of time series at different resolutions. However, geophysical time series often exhibits unavoidable data gaps stemming from diverse factors, impeding the straightforward implementation of ordinary MRA (OMRA). Moreover, geophysical time series is typically heterogeneous, as evidenced by the dynamic fluctuations in their precision. Regrettably, the prevailing approach of OMRA neglects to incorporate this aspect of heterogeneity. This study develops an extended MRA (EMRA) approach that solves for the missing values based on the best approximation in the temporal domain. The proposed method can directly analyze incomplete time series without prior interpolation and accounts for the formal errors of time series to improve the filtering performance. To validate the proposed approach, we use the EMRA method to extract crustal deformation signals from the daily position time series of 27 permanent global navigation satellite system (GNSS) stations in the Chinese mainland from 1999 to 2019. We compare the results with those obtained through OMRA using interpolation methods. The results reveal that EMRA can extract more signals than OMRA, particularly when considering formal errors. Repeated simulations further depict that the signals extracted by EMRA are closer to the simulated true signals than those by OMRA using interpolation methods.